Finite Group Databasebeta

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C42×C11×C37 #72185647

order6512
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 34560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C11×C37

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C11×C37
socle, prime radicalC22×C11×C37C22
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C8×C11×C37, C2×C42×C11×C37, C3×C42×C11×C37, …
maximal normal subgroup ofC4×C8×C11×C37, C2×C42×C11×C37, C3×C42×C11×C37, …
maximal quotient ofC4×C8×C11×C37, C2×C42×C11×C37, C3×C42×C11×C37, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.